The Batalin–Tyutin Formalism on the Collective Coordinates Quantization of the SU(2) Skyrme Model

Oliveira, W.; Neto, Jorge Ananias

doi:10.1142/s0217751x97002619

Cited by 26 publications

(57 citation statements)

References 14 publications

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“…As it has been stated before [23,24], there are more than one solution for equation (12). Thus, for a given second class system, there are so many corresponding first class systems which divert to it after gauge fixing.…”

Section: Bft Methodsmentioning

confidence: 85%

“…Most papers about these models are focused on the consistent canonical quantization and their quantum spectrum. This family of models were considered in several approaches including: the symplectic embedding [8,9,10,11], the BFT formalism [9,12,13,17,14,15,16], Stuckelberg field shifting [19,18] or mixed approaches based on first principles of the making gauge systems [9,18,20,21,22].…”

Section: Introductionmentioning

confidence: 99%

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First class models from linear and nonlinear second class constraints

et al. 2015

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Two models with linear and nonlinear second class constraints are considered and gauged by embedding in an extended phase space. These models are studied by considering a free non-relativistic particle on the hyper plane and hyper sphere in the configuration space. The gauged theory of the first model is obtained by converting the very second class system to the first class one, directly. In contrast, the first class system related to the free particle on the hyper sphere is derived with the help of the infinite BFT embedding procedure. We propose a practical formula, based on the simplified BFT method, which is practical in gauging linear and some nonlinear second class systems. As a result of gauging these two models, we show that in the conversion of second class constraints to the first class ones, the minimum number of phase space degrees of freedom for both systems is a pair of phase space coordinates. This pair is made up of a coordinate and its conjugate momentum for the first model, but the corresponding Poisson structure of the embedded non-relativistic particle on hyper sphere is a non-trivial one. We derive infinite correction terms for the Hamiltonian of the nonlinear constraints and an interacting gauged Hamiltonian is constructed by summing over them. At

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Section: Bft Methodsmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

First class models from linear and nonlinear second class constraints

et al. 2015

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“…In the next section, we reformulate the SU(2) Skyrme model as a gauge theory that, recently, has been intensively studied in the literature from many points of view [9,[18][19][20]22], using the symplectic gauge-invariant process.…”

Section: Symplectic Gauge-invariant Formalismmentioning

confidence: 99%

Gauging the SU(2) Skyrme model

2001

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In this paper the SU(2) Skyrme model will be reformulated as a gauge theory and the hidden symmetry will be investigated and explored in the energy spectrum computation. To this end we purpose a new constraint conversion scheme, based on the symplectic framework with the introduction of Wess-Zumino (WZ) terms in an unambiguous way. It is a positive feature not present on the BFFT constraint conversion. The Dirac's procedure for the first-class constraints is employed to quantize this gauge invariant nonlinear system and the energy spectrum is computed. The finding out shows the power of the symplectic gauge-invariant formalism when compared with another constraint conversion procedures present on the literature.

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“…Recently this BFT scheme has been applied to several areas of current interests such as the soliton models [14,15], high dense matter physics [16] and D-brane systems [17].…”

Section: Introductionmentioning

confidence: 99%